The heterogeneous pore space of porous media strongly affects the storage and migration of oil and gas in the reservoir. In this paper, the cross-correlation-based simulation (CCSIM) is combined with the three-step sample method to reconstruct stochastically 3D models of the heterogeneous porous media. Moreover, the two-point and multiple-point connectivity probability functions are used as vertical constraint conditions to select the boundary points of pore and matrix, respectively. The heterogeneities of pore spaces of four rock samples are investigated, and then our methods are tested on the four samples. Quantitative comparison is made by computing various statistical and petrophysical properties for the original samples, as well as the reconstructed model. It was found that the results from CCSIM-TSS are obviously better than that from CCSIM. Finally, the analysis of the distance (ANODI) was used to measure of the variability between the realizations of the four rock samples. The results demonstrated that the results from CCSIM-TSSmp are better than that from CCSIM-TSStp as the complexity of connectivity and heterogeneities of pore spaces increase.

Chinese Academy of Sciences [XDA14010304]
; National Natural Science Foundation of China [41404114, 41690132]
; National Program on Key Basic Research Project (973 Program) [2014CB239004]
; Strategic Priority Research Program of the Chinese Academy of Sciences [XDB10020302]